Binary Choice Models

$[7]$

Consider the following intercity mode choice model. Travelers have the option of choosing either the car or air modes for their trip. The parameters of the estimated logit model are presented in the table below:

$\backslash$table$[[,$Utility for Car,Utlity for Air$],[,$Param.,$t$ stat,Param.,$t$ stat$],[$Constant$,4\mathrm{.}77,6\mathrm{.}995,0,$fixed$],[$Travel Time $($mins$),-0\mathrm{.}03,-16\mathrm{.}926,-0\mathrm{.}03,-16\mathrm{.}926],[$Travel Cost $/$ Income $(\frac{\text{\$}}{\text{\$}}),-726\mathrm{.}35,-4\mathrm{.}28,-726\mathrm{.}35,-4\mathrm{.}28],[$Frequency of Flights $($per week$),0,$fixed,$0\mathrm{.}12,13\mathrm{.}414],[$Is Destination a Large City,$0,$fixed,$1\mathrm{.}5,5\mathrm{.}576],[$Travel Party Size $2^2,1\mathrm{.}75,5\mathrm{.}873,0,$fixed$],[1$ if destination city a large, $0$ otherwise,,,,$],[21$ if traveling in a group of $2$ or more people, $0$ otherwise,,,,$]]$

$($a$)$ Compute the money value of travel time $($VOTT$)$ for an average traveler $($Income $=$$$40,000$ in this intercity corridor using the above empirical specification. $[1]$

$($b$)$ It has been estimated that $1000$ persons travel independently from home city A to destination city B$.$ Both these cities are small, and the income of the travelers is $$40,000\mathrm{.}22$ flights are operated between the two cities every week. Using the above model, determine how many travelers will choose the air mode under each of the following three scenarios: $[6]$

$\backslash$table$[[$Scenario #$,$Description,,$],[,,$Air,Car,Air,Car,,$],[1,$Base case,$180,280,170,64,,],[2,$Increase in Airline Security,$220,280,170,64,,],[3,$Highway Tolls,$180,280,170,80,,]]$